Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(169,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.169 |
Dual form | 210.2.g.b.169.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | + | 2.00000i | 0.447214 | + | 0.894427i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.00000 | − | 1.00000i | 0.632456 | − | 0.316228i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | − | 8.00000i | − | 1.66812i | −0.551677 | − | 0.834058i | \(-0.686012\pi\) | ||
0.551677 | − | 0.834058i | \(-0.313988\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 1.00000 | + | 2.00000i | 0.182574 | + | 0.365148i | ||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −2.00000 | + | 1.00000i | −0.338062 | + | 0.169031i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | − | 6.00000i | − | 0.973329i | ||||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | −2.00000 | + | 1.00000i | −0.316228 | + | 0.158114i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | −1.00000 | − | 2.00000i | −0.149071 | − | 0.298142i | ||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | − | 6.00000i | − | 0.832050i | ||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.00000 | + | 4.00000i | 0.269680 | + | 0.539360i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 2.00000 | − | 1.00000i | 0.258199 | − | 0.129099i | ||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 2.00000i | 0.254000i | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −12.0000 | + | 6.00000i | −1.48842 | + | 0.744208i | ||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 4.00000i | 0.485071i | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 1.00000 | + | 2.00000i | 0.119523 | + | 0.239046i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | − | 14.0000i | − | 1.63858i | −0.573382 | − | 0.819288i | \(-0.694369\pi\) | ||
0.573382 | − | 0.819288i | \(-0.305631\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | −6.00000 | −0.688247 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 6.00000i | 0.679366i | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 2.00000i | − | 0.220863i | ||||||
\(83\) | − | 8.00000i | − | 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 8.00000 | − | 4.00000i | 0.867722 | − | 0.433861i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | − | 6.00000i | − | 0.643268i | ||||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −2.00000 | + | 1.00000i | −0.210819 | + | 0.105409i | ||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | − | 2.00000i | − | 0.207390i | ||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 6.00000 | + | 12.0000i | 0.615587 | + | 1.23117i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | − | 4.00000i | − | 0.396059i | ||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | −1.00000 | − | 2.00000i | −0.0975900 | − | 0.195180i | ||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 4.00000 | − | 2.00000i | 0.381385 | − | 0.190693i | ||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 6.00000 | 0.561951 | ||||||||
\(115\) | 16.0000 | − | 8.00000i | 1.49201 | − | 0.746004i | ||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | − | 6.00000i | − | 0.554700i | ||||||
\(118\) | − | 8.00000i | − | 0.736460i | ||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | −1.00000 | − | 2.00000i | −0.0912871 | − | 0.182574i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | 2.00000i | 0.180334i | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | − | 4.00000i | − | 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 6.00000 | + | 12.0000i | 0.526235 | + | 1.05247i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | − | 2.00000i | − | 0.174078i | ||||||
\(133\) | 6.00000i | 0.520266i | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 2.00000 | − | 1.00000i | 0.172133 | − | 0.0860663i | ||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | − | 8.00000i | − | 0.681005i | ||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 2.00000 | − | 1.00000i | 0.169031 | − | 0.0845154i | ||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | 12.0000i | 1.00349i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −6.00000 | − | 12.0000i | −0.498273 | − | 0.996546i | ||||
\(146\) | −14.0000 | −1.15865 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 4.00000i | 0.328798i | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −3.00000 | + | 4.00000i | −0.244949 | + | 0.326599i | ||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 6.00000i | 0.486664i | ||||||||
\(153\) | 4.00000i | 0.323381i | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | −2.00000 | − | 4.00000i | −0.160644 | − | 0.321288i | ||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | 22.0000i | 1.75579i | 0.478852 | + | 0.877896i | \(0.341053\pi\) | ||||
−0.478852 | + | 0.877896i | \(0.658947\pi\) | |||||||
\(158\) | − | 12.0000i | − | 0.954669i | ||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 2.00000 | − | 1.00000i | 0.158114 | − | 0.0790569i | ||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | −4.00000 | + | 2.00000i | −0.311400 | + | 0.155700i | ||||
\(166\) | −8.00000 | −0.620920 | ||||||||
\(167\) | 12.0000i | 0.928588i | 0.885681 | + | 0.464294i | \(0.153692\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(168\) | − | 1.00000i | − | 0.0771517i | ||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | −4.00000 | − | 8.00000i | −0.306786 | − | 0.613572i | ||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | − | 4.00000i | − | 0.304997i | ||||||
\(173\) | 8.00000i | 0.608229i | 0.952636 | + | 0.304114i | \(0.0983605\pi\) | ||||
−0.952636 | + | 0.304114i | \(0.901639\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | −4.00000 | − | 3.00000i | −0.302372 | − | 0.226779i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 8.00000i | 0.601317i | ||||||||
\(178\) | − | 10.0000i | − | 0.749532i | ||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | 1.00000 | + | 2.00000i | 0.0745356 | + | 0.149071i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 6.00000i | 0.444750i | ||||||||
\(183\) | − | 10.0000i | − | 0.739221i | ||||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | 8.00000 | − | 4.00000i | 0.588172 | − | 0.294086i | ||||
\(186\) | −2.00000 | −0.146647 | ||||||||
\(187\) | − | 8.00000i | − | 0.585018i | ||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 12.0000 | − | 6.00000i | 0.870572 | − | 0.435286i | ||||
\(191\) | −18.0000 | −1.30243 | −0.651217 | − | 0.758891i | \(-0.725741\pi\) | ||||
−0.651217 | + | 0.758891i | \(0.725741\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | − | 8.00000i | − | 0.575853i | −0.957653 | − | 0.287926i | \(-0.907034\pi\) | ||
0.957653 | − | 0.287926i | \(-0.0929658\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | −6.00000 | − | 12.0000i | −0.429669 | − | 0.859338i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 2.00000i | 0.142134i | ||||||||
\(199\) | −6.00000 | −0.425329 | −0.212664 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212664 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(200\) | −4.00000 | − | 3.00000i | −0.282843 | − | 0.212132i | ||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | − | 10.0000i | − | 0.703598i | ||||||
\(203\) | − | 6.00000i | − | 0.421117i | ||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 2.00000 | + | 4.00000i | 0.139686 | + | 0.279372i | ||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 8.00000i | 0.556038i | ||||||||
\(208\) | 6.00000i | 0.416025i | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | −2.00000 | + | 1.00000i | −0.138013 | + | 0.0690066i | ||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | − | 6.00000i | − | 0.411113i | ||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | −8.00000 | + | 4.00000i | −0.545595 | + | 0.272798i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | − | 14.0000i | − | 0.948200i | ||||||
\(219\) | 14.0000 | 0.946032 | ||||||||
\(220\) | −2.00000 | − | 4.00000i | −0.134840 | − | 0.269680i | ||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | − | 4.00000i | − | 0.268462i | ||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 8.00000i | 0.530979i | 0.964114 | + | 0.265489i | \(0.0855335\pi\) | ||||
−0.964114 | + | 0.265489i | \(0.914466\pi\) | |||||||
\(228\) | − | 6.00000i | − | 0.397360i | ||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | −8.00000 | − | 16.0000i | −0.527504 | − | 1.05501i | ||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | − | 10.0000i | − | 0.655122i | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | −6.00000 | −0.392232 | ||||||||
\(235\) | 16.0000 | − | 8.00000i | 1.04372 | − | 0.521862i | ||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | 12.0000i | 0.779484i | ||||||||
\(238\) | − | 4.00000i | − | 0.259281i | ||||||
\(239\) | −26.0000 | −1.68180 | −0.840900 | − | 0.541190i | \(-0.817974\pi\) | ||||
−0.840900 | + | 0.541190i | \(0.817974\pi\) | |||||||
\(240\) | −2.00000 | + | 1.00000i | −0.129099 | + | 0.0645497i | ||||
\(241\) | −26.0000 | −1.67481 | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||||
−0.837404 | + | 0.546585i | \(0.815928\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | −1.00000 | − | 2.00000i | −0.0638877 | − | 0.127775i | ||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 36.0000i | 2.29063i | ||||||||
\(248\) | − | 2.00000i | − | 0.127000i | ||||||
\(249\) | 8.00000 | 0.506979 | ||||||||
\(250\) | −2.00000 | + | 11.0000i | −0.126491 | + | 0.695701i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | − | 16.0000i | − | 1.00591i | ||||||
\(254\) | −4.00000 | −0.250982 | ||||||||
\(255\) | 4.00000 | + | 8.00000i | 0.250490 | + | 0.500979i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 4.00000i | 0.249029i | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 12.0000 | − | 6.00000i | 0.744208 | − | 0.372104i | ||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 12.0000i | 0.741362i | ||||||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | −2.00000 | −0.123091 | ||||||||
\(265\) | −12.0000 | + | 6.00000i | −0.737154 | + | 0.368577i | ||||
\(266\) | 6.00000 | 0.367884 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | −1.00000 | − | 2.00000i | −0.0608581 | − | 0.121716i | ||||
\(271\) | 10.0000 | 0.607457 | 0.303728 | − | 0.952759i | \(-0.401768\pi\) | ||||
0.303728 | + | 0.952759i | \(0.401768\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | − | 6.00000i | − | 0.363137i | ||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −6.00000 | + | 8.00000i | −0.361814 | + | 0.482418i | ||||
\(276\) | −8.00000 | −0.481543 | ||||||||
\(277\) | − | 28.0000i | − | 1.68236i | −0.540758 | − | 0.841178i | \(-0.681862\pi\) | ||
0.540758 | − | 0.841178i | \(-0.318138\pi\) | |||||||
\(278\) | − | 14.0000i | − | 0.839664i | ||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | −1.00000 | − | 2.00000i | −0.0597614 | − | 0.119523i | ||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | − | 8.00000i | − | 0.476393i | ||||||
\(283\) | 20.0000i | 1.18888i | 0.804141 | + | 0.594438i | \(0.202626\pi\) | ||||
−0.804141 | + | 0.594438i | \(0.797374\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | −12.0000 | + | 6.00000i | −0.710819 | + | 0.355409i | ||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | 2.00000i | 0.118056i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −12.0000 | + | 6.00000i | −0.704664 | + | 0.352332i | ||||
\(291\) | −10.0000 | −0.586210 | ||||||||
\(292\) | 14.0000i | 0.819288i | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 8.00000 | + | 16.0000i | 0.465778 | + | 0.931556i | ||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | − | 2.00000i | − | 0.116052i | ||||||
\(298\) | 10.0000i | 0.579284i | ||||||||
\(299\) | 48.0000 | 2.77591 | ||||||||
\(300\) | 4.00000 | + | 3.00000i | 0.230940 | + | 0.173205i | ||||
\(301\) | −4.00000 | −0.230556 | ||||||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | 10.0000i | 0.574485i | ||||||||
\(304\) | 6.00000 | 0.344124 | ||||||||
\(305\) | −10.0000 | − | 20.0000i | −0.572598 | − | 1.14520i | ||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | 12.0000i | 0.684876i | 0.939540 | + | 0.342438i | \(0.111253\pi\) | ||||
−0.939540 | + | 0.342438i | \(0.888747\pi\) | |||||||
\(308\) | − | 2.00000i | − | 0.113961i | ||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | −4.00000 | + | 2.00000i | −0.227185 | + | 0.113592i | ||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | − | 6.00000i | − | 0.339683i | ||||||
\(313\) | − | 2.00000i | − | 0.113047i | −0.998401 | − | 0.0565233i | \(-0.981998\pi\) | ||
0.998401 | − | 0.0565233i | \(-0.0180015\pi\) | |||||||
\(314\) | 22.0000 | 1.24153 | ||||||||
\(315\) | 2.00000 | − | 1.00000i | 0.112687 | − | 0.0563436i | ||||
\(316\) | −12.0000 | −0.675053 | ||||||||
\(317\) | 2.00000i | 0.112331i | 0.998421 | + | 0.0561656i | \(0.0178875\pi\) | ||||
−0.998421 | + | 0.0561656i | \(0.982113\pi\) | |||||||
\(318\) | 6.00000i | 0.336463i | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | −1.00000 | − | 2.00000i | −0.0559017 | − | 0.111803i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | − | 8.00000i | − | 0.445823i | ||||||
\(323\) | − | 24.0000i | − | 1.33540i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −24.0000 | − | 18.0000i | −1.33128 | − | 0.998460i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 14.0000i | 0.774202i | ||||||||
\(328\) | 2.00000i | 0.110432i | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 2.00000 | + | 4.00000i | 0.110096 | + | 0.220193i | ||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 8.00000i | 0.439057i | ||||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 16.0000 | − | 8.00000i | 0.874173 | − | 0.437087i | ||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 8.00000i | 0.435788i | 0.975972 | + | 0.217894i | \(0.0699187\pi\) | ||||
−0.975972 | + | 0.217894i | \(0.930081\pi\) | |||||||
\(338\) | 23.0000i | 1.25104i | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | −8.00000 | + | 4.00000i | −0.433861 | + | 0.216930i | ||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 6.00000i | 0.324443i | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 8.00000 | + | 16.0000i | 0.430706 | + | 0.861411i | ||||
\(346\) | 8.00000 | 0.430083 | ||||||||
\(347\) | − | 36.0000i | − | 1.93258i | −0.257454 | − | 0.966291i | \(-0.582883\pi\) | ||
0.257454 | − | 0.966291i | \(-0.417117\pi\) | |||||||
\(348\) | 6.00000i | 0.321634i | ||||||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | −3.00000 | + | 4.00000i | −0.160357 | + | 0.213809i | ||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | − | 2.00000i | − | 0.106600i | ||||||
\(353\) | 20.0000i | 1.06449i | 0.846590 | + | 0.532246i | \(0.178652\pi\) | ||||
−0.846590 | + | 0.532246i | \(0.821348\pi\) | |||||||
\(354\) | 8.00000 | 0.425195 | ||||||||
\(355\) | −6.00000 | − | 12.0000i | −0.318447 | − | 0.636894i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 4.00000i | 0.211702i | ||||||||
\(358\) | 10.0000i | 0.528516i | ||||||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | 2.00000 | − | 1.00000i | 0.105409 | − | 0.0527046i | ||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | − | 2.00000i | − | 0.105118i | ||||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 6.00000 | 0.314485 | ||||||||
\(365\) | 28.0000 | − | 14.0000i | 1.46559 | − | 0.732793i | ||||
\(366\) | −10.0000 | −0.522708 | ||||||||
\(367\) | 32.0000i | 1.67039i | 0.549957 | + | 0.835193i | \(0.314644\pi\) | ||||
−0.549957 | + | 0.835193i | \(0.685356\pi\) | |||||||
\(368\) | − | 8.00000i | − | 0.417029i | ||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | −4.00000 | − | 8.00000i | −0.207950 | − | 0.415900i | ||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | − | 24.0000i | − | 1.24267i | −0.783544 | − | 0.621336i | \(-0.786590\pi\) | ||
0.783544 | − | 0.621336i | \(-0.213410\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | 2.00000 | − | 11.0000i | 0.103280 | − | 0.568038i | ||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | − | 36.0000i | − | 1.85409i | ||||||
\(378\) | − | 1.00000i | − | 0.0514344i | ||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | −6.00000 | − | 12.0000i | −0.307794 | − | 0.615587i | ||||
\(381\) | 4.00000 | 0.204926 | ||||||||
\(382\) | 18.0000i | 0.920960i | ||||||||
\(383\) | 20.0000i | 1.02195i | 0.859595 | + | 0.510976i | \(0.170716\pi\) | ||||
−0.859595 | + | 0.510976i | \(0.829284\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.00000 | + | 2.00000i | −0.203859 | + | 0.101929i | ||||
\(386\) | −8.00000 | −0.407189 | ||||||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | − | 10.0000i | − | 0.507673i | ||||||
\(389\) | −2.00000 | −0.101404 | −0.0507020 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507020 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(390\) | −12.0000 | + | 6.00000i | −0.607644 | + | 0.303822i | ||||
\(391\) | −32.0000 | −1.61831 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | −2.00000 | −0.100759 | ||||||||
\(395\) | 12.0000 | + | 24.0000i | 0.603786 | + | 1.20757i | ||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | 6.00000i | 0.300753i | ||||||||
\(399\) | −6.00000 | −0.300376 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | −14.0000 | −0.699127 | −0.349563 | − | 0.936913i | \(-0.613670\pi\) | ||||
−0.349563 | + | 0.936913i | \(0.613670\pi\) | |||||||
\(402\) | − | 8.00000i | − | 0.399004i | ||||||
\(403\) | − | 12.0000i | − | 0.597763i | ||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | − | 8.00000i | − | 0.396545i | ||||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | 4.00000 | − | 2.00000i | 0.197546 | − | 0.0987730i | ||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | 8.00000i | 0.393654i | ||||||||
\(414\) | 8.00000 | 0.393179 | ||||||||
\(415\) | 16.0000 | − | 8.00000i | 0.785409 | − | 0.392705i | ||||
\(416\) | 6.00000 | 0.294174 | ||||||||
\(417\) | 14.0000i | 0.685583i | ||||||||
\(418\) | − | 12.0000i | − | 0.586939i | ||||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 1.00000 | + | 2.00000i | 0.0487950 | + | 0.0975900i | ||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 16.0000 | + | 12.0000i | 0.776114 | + | 0.582086i | ||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | − | 10.0000i | − | 0.483934i | ||||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | −12.0000 | −0.579365 | ||||||||
\(430\) | 4.00000 | + | 8.00000i | 0.192897 | + | 0.385794i | ||||
\(431\) | 2.00000 | 0.0963366 | 0.0481683 | − | 0.998839i | \(-0.484662\pi\) | ||||
0.0481683 | + | 0.998839i | \(0.484662\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 26.0000i | − | 1.24948i | −0.780833 | − | 0.624740i | \(-0.785205\pi\) | ||
0.780833 | − | 0.624740i | \(-0.214795\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 12.0000 | − | 6.00000i | 0.575356 | − | 0.287678i | ||||
\(436\) | −14.0000 | −0.670478 | ||||||||
\(437\) | − | 48.0000i | − | 2.29615i | ||||||
\(438\) | − | 14.0000i | − | 0.668946i | ||||||
\(439\) | 18.0000 | 0.859093 | 0.429547 | − | 0.903045i | \(-0.358673\pi\) | ||||
0.429547 | + | 0.903045i | \(0.358673\pi\) | |||||||
\(440\) | −4.00000 | + | 2.00000i | −0.190693 | + | 0.0953463i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − | 24.0000i | − | 1.14156i | ||||||
\(443\) | − | 12.0000i | − | 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | −4.00000 | −0.189832 | ||||||||
\(445\) | 10.0000 | + | 20.0000i | 0.474045 | + | 0.948091i | ||||
\(446\) | −8.00000 | −0.378811 | ||||||||
\(447\) | − | 10.0000i | − | 0.472984i | ||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | −4.00000 | − | 3.00000i | −0.188562 | − | 0.141421i | ||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | − | 8.00000i | − | 0.375873i | ||||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | −6.00000 | − | 12.0000i | −0.281284 | − | 0.562569i | ||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | − | 28.0000i | − | 1.30978i | −0.755722 | − | 0.654892i | \(-0.772714\pi\) | ||
0.755722 | − | 0.654892i | \(-0.227286\pi\) | |||||||
\(458\) | 14.0000i | 0.654177i | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | −16.0000 | + | 8.00000i | −0.746004 | + | 0.373002i | ||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 2.00000i | 0.0930484i | ||||||||
\(463\) | 36.0000i | 1.67306i | 0.547920 | + | 0.836531i | \(0.315420\pi\) | ||||
−0.547920 | + | 0.836531i | \(0.684580\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 4.00000 | − | 2.00000i | 0.185496 | − | 0.0927478i | ||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | 24.0000i | 1.11059i | 0.831654 | + | 0.555294i | \(0.187394\pi\) | ||||
−0.831654 | + | 0.555294i | \(0.812606\pi\) | |||||||
\(468\) | 6.00000i | 0.277350i | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | −8.00000 | − | 16.0000i | −0.369012 | − | 0.738025i | ||||
\(471\) | −22.0000 | −1.01371 | ||||||||
\(472\) | 8.00000i | 0.368230i | ||||||||
\(473\) | 8.00000i | 0.367840i | ||||||||
\(474\) | 12.0000 | 0.551178 | ||||||||
\(475\) | −18.0000 | + | 24.0000i | −0.825897 | + | 1.10120i | ||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | − | 6.00000i | − | 0.274721i | ||||||
\(478\) | 26.0000i | 1.18921i | ||||||||
\(479\) | −8.00000 | −0.365529 | −0.182765 | − | 0.983157i | \(-0.558505\pi\) | ||||
−0.182765 | + | 0.983157i | \(0.558505\pi\) | |||||||
\(480\) | 1.00000 | + | 2.00000i | 0.0456435 | + | 0.0912871i | ||||
\(481\) | 24.0000 | 1.09431 | ||||||||
\(482\) | 26.0000i | 1.18427i | ||||||||
\(483\) | 8.00000i | 0.364013i | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | −20.0000 | + | 10.0000i | −0.908153 | + | 0.454077i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 12.0000i | − | 0.543772i | −0.962329 | − | 0.271886i | \(-0.912353\pi\) | ||
0.962329 | − | 0.271886i | \(-0.0876473\pi\) | |||||||
\(488\) | − | 10.0000i | − | 0.452679i | ||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | −2.00000 | + | 1.00000i | −0.0903508 | + | 0.0451754i | ||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | − | 2.00000i | − | 0.0901670i | ||||||
\(493\) | 24.0000i | 1.08091i | ||||||||
\(494\) | 36.0000 | 1.61972 | ||||||||
\(495\) | −2.00000 | − | 4.00000i | −0.0898933 | − | 0.179787i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | − | 6.00000i | − | 0.269137i | ||||||
\(498\) | − | 8.00000i | − | 0.358489i | ||||||
\(499\) | 12.0000 | 0.537194 | 0.268597 | − | 0.963253i | \(-0.413440\pi\) | ||||
0.268597 | + | 0.963253i | \(0.413440\pi\) | |||||||
\(500\) | 11.0000 | + | 2.00000i | 0.491935 | + | 0.0894427i | ||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 10.0000 | + | 20.0000i | 0.444994 | + | 0.889988i | ||||
\(506\) | −16.0000 | −0.711287 | ||||||||
\(507\) | − | 23.0000i | − | 1.02147i | ||||||
\(508\) | 4.00000i | 0.177471i | ||||||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 8.00000 | − | 4.00000i | 0.354246 | − | 0.177123i | ||||
\(511\) | 14.0000 | 0.619324 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 6.00000i | − | 0.264906i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.0000 | + | 8.00000i | −0.705044 | + | 0.352522i | ||||
\(516\) | 4.00000 | 0.176090 | ||||||||
\(517\) | − | 16.0000i | − | 0.703679i | ||||||
\(518\) | − | 4.00000i | − | 0.175750i | ||||||
\(519\) | −8.00000 | −0.351161 | ||||||||
\(520\) | −6.00000 | − | 12.0000i | −0.263117 | − | 0.526235i | ||||
\(521\) | −26.0000 | −1.13908 | −0.569540 | − | 0.821963i | \(-0.692879\pi\) | ||||
−0.569540 | + | 0.821963i | \(0.692879\pi\) | |||||||
\(522\) | − | 6.00000i | − | 0.262613i | ||||||
\(523\) | − | 28.0000i | − | 1.22435i | −0.790721 | − | 0.612177i | \(-0.790294\pi\) | ||
0.790721 | − | 0.612177i | \(-0.209706\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 3.00000 | − | 4.00000i | 0.130931 | − | 0.174574i | ||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | 8.00000i | 0.348485i | ||||||||
\(528\) | 2.00000i | 0.0870388i | ||||||||
\(529\) | −41.0000 | −1.78261 | ||||||||
\(530\) | 6.00000 | + | 12.0000i | 0.260623 | + | 0.521247i | ||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | − | 6.00000i | − | 0.260133i | ||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 10.0000 | 0.432742 | ||||||||
\(535\) | 24.0000 | − | 12.0000i | 1.03761 | − | 0.518805i | ||||
\(536\) | 8.00000 | 0.345547 | ||||||||
\(537\) | − | 10.0000i | − | 0.431532i | ||||||
\(538\) | 18.0000i | 0.776035i | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | − | 10.0000i | − | 0.429537i | ||||||
\(543\) | 2.00000i | 0.0858282i | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 14.0000 | + | 28.0000i | 0.599694 | + | 1.19939i | ||||
\(546\) | −6.00000 | −0.256776 | ||||||||
\(547\) | − | 40.0000i | − | 1.71028i | −0.518400 | − | 0.855138i | \(-0.673472\pi\) | ||
0.518400 | − | 0.855138i | \(-0.326528\pi\) | |||||||
\(548\) | − | 6.00000i | − | 0.256307i | ||||||
\(549\) | 10.0000 | 0.426790 | ||||||||
\(550\) | 8.00000 | + | 6.00000i | 0.341121 | + | 0.255841i | ||||
\(551\) | −36.0000 | −1.53365 | ||||||||
\(552\) | 8.00000i | 0.340503i | ||||||||
\(553\) | 12.0000i | 0.510292i | ||||||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | 4.00000 | + | 8.00000i | 0.169791 | + | 0.339581i | ||||
\(556\) | −14.0000 | −0.593732 | ||||||||
\(557\) | 42.0000i | 1.77960i | 0.456354 | + | 0.889799i | \(0.349155\pi\) | ||||
−0.456354 | + | 0.889799i | \(0.650845\pi\) | |||||||
\(558\) | − | 2.00000i | − | 0.0846668i | ||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | −2.00000 | + | 1.00000i | −0.0845154 | + | 0.0422577i | ||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | − | 30.0000i | − | 1.26547i | ||||||
\(563\) | − | 4.00000i | − | 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | −8.00000 | −0.336861 | ||||||||
\(565\) | −12.0000 | + | 6.00000i | −0.504844 | + | 0.252422i | ||||
\(566\) | 20.0000 | 0.840663 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 46.0000 | 1.92842 | 0.964210 | − | 0.265139i | \(-0.0854179\pi\) | ||||
0.964210 | + | 0.265139i | \(0.0854179\pi\) | |||||||
\(570\) | 6.00000 | + | 12.0000i | 0.251312 | + | 0.502625i | ||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | − | 12.0000i | − | 0.501745i | ||||||
\(573\) | − | 18.0000i | − | 0.751961i | ||||||
\(574\) | 2.00000 | 0.0834784 | ||||||||
\(575\) | 32.0000 | + | 24.0000i | 1.33449 | + | 1.00087i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 26.0000i | 1.08239i | 0.840896 | + | 0.541197i | \(0.182029\pi\) | ||||
−0.840896 | + | 0.541197i | \(0.817971\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 8.00000 | 0.332469 | ||||||||
\(580\) | 6.00000 | + | 12.0000i | 0.249136 | + | 0.498273i | ||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 10.0000i | 0.414513i | ||||||||
\(583\) | 12.0000i | 0.496989i | ||||||||
\(584\) | 14.0000 | 0.579324 | ||||||||
\(585\) | 12.0000 | − | 6.00000i | 0.496139 | − | 0.248069i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 1.00000i | 0.0412393i | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 16.0000 | − | 8.00000i | 0.658710 | − | 0.329355i | ||||
\(591\) | 2.00000 | 0.0822690 | ||||||||
\(592\) | − | 4.00000i | − | 0.164399i | ||||||
\(593\) | 12.0000i | 0.492781i | 0.969171 | + | 0.246390i | \(0.0792446\pi\) | ||||
−0.969171 | + | 0.246390i | \(0.920755\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 4.00000 | + | 8.00000i | 0.163984 | + | 0.327968i | ||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | − | 6.00000i | − | 0.245564i | ||||||
\(598\) | − | 48.0000i | − | 1.96287i | ||||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 3.00000 | − | 4.00000i | 0.122474 | − | 0.163299i | ||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 4.00000i | 0.163028i | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −7.00000 | − | 14.0000i | −0.284590 | − | 0.569181i | ||||
\(606\) | 10.0000 | 0.406222 | ||||||||
\(607\) | − | 8.00000i | − | 0.324710i | −0.986732 | − | 0.162355i | \(-0.948091\pi\) | ||
0.986732 | − | 0.162355i | \(-0.0519090\pi\) | |||||||
\(608\) | − | 6.00000i | − | 0.243332i | ||||||
\(609\) | 6.00000 | 0.243132 | ||||||||
\(610\) | −20.0000 | + | 10.0000i | −0.809776 | + | 0.404888i | ||||
\(611\) | 48.0000 | 1.94187 | ||||||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | 28.0000i | 1.13091i | 0.824779 | + | 0.565455i | \(0.191299\pi\) | ||||
−0.824779 | + | 0.565455i | \(0.808701\pi\) | |||||||
\(614\) | 12.0000 | 0.484281 | ||||||||
\(615\) | −4.00000 | + | 2.00000i | −0.161296 | + | 0.0806478i | ||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | 26.0000i | 1.04672i | 0.852111 | + | 0.523360i | \(0.175322\pi\) | ||||
−0.852111 | + | 0.523360i | \(0.824678\pi\) | |||||||
\(618\) | 8.00000i | 0.321807i | ||||||||
\(619\) | 22.0000 | 0.884255 | 0.442127 | − | 0.896952i | \(-0.354224\pi\) | ||||
0.442127 | + | 0.896952i | \(0.354224\pi\) | |||||||
\(620\) | 2.00000 | + | 4.00000i | 0.0803219 | + | 0.160644i | ||||
\(621\) | −8.00000 | −0.321029 | ||||||||
\(622\) | − | 24.0000i | − | 0.962312i | ||||||
\(623\) | 10.0000i | 0.400642i | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −2.00000 | −0.0799361 | ||||||||
\(627\) | 12.0000i | 0.479234i | ||||||||
\(628\) | − | 22.0000i | − | 0.877896i | ||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | −1.00000 | − | 2.00000i | −0.0398410 | − | 0.0796819i | ||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | 12.0000i | 0.477334i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.00000 | 0.0794301 | ||||||||
\(635\) | 8.00000 | − | 4.00000i | 0.317470 | − | 0.158735i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | − | 6.00000i | − | 0.237729i | ||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | −2.00000 | + | 1.00000i | −0.0790569 | + | 0.0395285i | ||||
\(641\) | 14.0000 | 0.552967 | 0.276483 | − | 0.961019i | \(-0.410831\pi\) | ||||
0.276483 | + | 0.961019i | \(0.410831\pi\) | |||||||
\(642\) | − | 12.0000i | − | 0.473602i | ||||||
\(643\) | 12.0000i | 0.473234i | 0.971603 | + | 0.236617i | \(0.0760386\pi\) | ||||
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | −8.00000 | −0.315244 | ||||||||
\(645\) | −4.00000 | − | 8.00000i | −0.157500 | − | 0.315000i | ||||
\(646\) | −24.0000 | −0.944267 | ||||||||
\(647\) | − | 36.0000i | − | 1.41531i | −0.706560 | − | 0.707653i | \(-0.749754\pi\) | ||
0.706560 | − | 0.707653i | \(-0.250246\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | −18.0000 | + | 24.0000i | −0.706018 | + | 0.941357i | ||||
\(651\) | 2.00000 | 0.0783862 | ||||||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | 34.0000i | 1.33052i | 0.746611 | + | 0.665261i | \(0.231680\pi\) | ||||
−0.746611 | + | 0.665261i | \(0.768320\pi\) | |||||||
\(654\) | 14.0000 | 0.547443 | ||||||||
\(655\) | −12.0000 | − | 24.0000i | −0.468879 | − | 0.937758i | ||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 14.0000i | 0.546192i | ||||||||
\(658\) | − | 8.00000i | − | 0.311872i | ||||||
\(659\) | 26.0000 | 1.01282 | 0.506408 | − | 0.862294i | \(-0.330973\pi\) | ||||
0.506408 | + | 0.862294i | \(0.330973\pi\) | |||||||
\(660\) | 4.00000 | − | 2.00000i | 0.155700 | − | 0.0778499i | ||||
\(661\) | 38.0000 | 1.47803 | 0.739014 | − | 0.673690i | \(-0.235292\pi\) | ||||
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | 8.00000i | 0.310929i | ||||||||
\(663\) | 24.0000i | 0.932083i | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | −12.0000 | + | 6.00000i | −0.465340 | + | 0.232670i | ||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 48.0000i | 1.85857i | ||||||||
\(668\) | − | 12.0000i | − | 0.464294i | ||||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | −8.00000 | − | 16.0000i | −0.309067 | − | 0.618134i | ||||
\(671\) | −20.0000 | −0.772091 | ||||||||
\(672\) | 1.00000i | 0.0385758i | ||||||||
\(673\) | 12.0000i | 0.462566i | 0.972887 | + | 0.231283i | \(0.0742923\pi\) | ||||
−0.972887 | + | 0.231283i | \(0.925708\pi\) | |||||||
\(674\) | 8.00000 | 0.308148 | ||||||||
\(675\) | 4.00000 | + | 3.00000i | 0.153960 | + | 0.115470i | ||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | − | 40.0000i | − | 1.53732i | −0.639655 | − | 0.768662i | \(-0.720923\pi\) | ||
0.639655 | − | 0.768662i | \(-0.279077\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | −10.0000 | −0.383765 | ||||||||
\(680\) | 4.00000 | + | 8.00000i | 0.153393 | + | 0.306786i | ||||
\(681\) | −8.00000 | −0.306561 | ||||||||
\(682\) | 4.00000i | 0.153168i | ||||||||
\(683\) | 4.00000i | 0.153056i | 0.997067 | + | 0.0765279i | \(0.0243834\pi\) | ||||
−0.997067 | + | 0.0765279i | \(0.975617\pi\) | |||||||
\(684\) | 6.00000 | 0.229416 | ||||||||
\(685\) | −12.0000 | + | 6.00000i | −0.458496 | + | 0.229248i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | − | 14.0000i | − | 0.534133i | ||||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 16.0000 | − | 8.00000i | 0.609110 | − | 0.304555i | ||||
\(691\) | −2.00000 | −0.0760836 | −0.0380418 | − | 0.999276i | \(-0.512112\pi\) | ||||
−0.0380418 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(692\) | − | 8.00000i | − | 0.304114i | ||||||
\(693\) | − | 2.00000i | − | 0.0759737i | ||||||
\(694\) | −36.0000 | −1.36654 | ||||||||
\(695\) | 14.0000 | + | 28.0000i | 0.531050 | + | 1.06210i | ||||
\(696\) | 6.00000 | 0.227429 | ||||||||
\(697\) | − | 8.00000i | − | 0.303022i | ||||||
\(698\) | − | 26.0000i | − | 0.984115i | ||||||
\(699\) | 10.0000 | 0.378235 | ||||||||
\(700\) | 4.00000 | + | 3.00000i | 0.151186 | + | 0.113389i | ||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | − | 6.00000i | − | 0.226455i | ||||||
\(703\) | − | 24.0000i | − | 0.905177i | ||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 8.00000 | + | 16.0000i | 0.301297 | + | 0.602595i | ||||
\(706\) | 20.0000 | 0.752710 | ||||||||
\(707\) | 10.0000i | 0.376089i | ||||||||
\(708\) | − | 8.00000i | − | 0.300658i | ||||||
\(709\) | 6.00000 | 0.225335 | 0.112667 | − | 0.993633i | \(-0.464061\pi\) | ||||
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | −12.0000 | + | 6.00000i | −0.450352 | + | 0.225176i | ||||
\(711\) | −12.0000 | −0.450035 | ||||||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 16.0000i | 0.599205i | ||||||||
\(714\) | 4.00000 | 0.149696 | ||||||||
\(715\) | −24.0000 | + | 12.0000i | −0.897549 | + | 0.448775i | ||||
\(716\) | 10.0000 | 0.373718 | ||||||||
\(717\) | − | 26.0000i | − | 0.970988i | ||||||
\(718\) | 6.00000i | 0.223918i | ||||||||
\(719\) | 4.00000 | 0.149175 | 0.0745874 | − | 0.997214i | \(-0.476236\pi\) | ||||
0.0745874 | + | 0.997214i | \(0.476236\pi\) | |||||||
\(720\) | −1.00000 | − | 2.00000i | −0.0372678 | − | 0.0745356i | ||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | − | 26.0000i | − | 0.966950i | ||||||
\(724\) | −2.00000 | −0.0743294 | ||||||||
\(725\) | 18.0000 | − | 24.0000i | 0.668503 | − | 0.891338i | ||||
\(726\) | −7.00000 | −0.259794 | ||||||||
\(727\) | − | 24.0000i | − | 0.890111i | −0.895503 | − | 0.445055i | \(-0.853184\pi\) | ||
0.895503 | − | 0.445055i | \(-0.146816\pi\) | |||||||
\(728\) | − | 6.00000i | − | 0.222375i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −14.0000 | − | 28.0000i | −0.518163 | − | 1.03633i | ||||
\(731\) | 16.0000 | 0.591781 | ||||||||
\(732\) | 10.0000i | 0.369611i | ||||||||
\(733\) | 14.0000i | 0.517102i | 0.965998 | + | 0.258551i | \(0.0832450\pi\) | ||||
−0.965998 | + | 0.258551i | \(0.916755\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | 2.00000 | − | 1.00000i | 0.0737711 | − | 0.0368856i | ||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | − | 16.0000i | − | 0.589368i | ||||||
\(738\) | 2.00000i | 0.0736210i | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | −8.00000 | + | 4.00000i | −0.294086 | + | 0.147043i | ||||
\(741\) | −36.0000 | −1.32249 | ||||||||
\(742\) | 6.00000i | 0.220267i | ||||||||
\(743\) | − | 48.0000i | − | 1.76095i | −0.474093 | − | 0.880475i | \(-0.657224\pi\) | ||
0.474093 | − | 0.880475i | \(-0.342776\pi\) | |||||||
\(744\) | 2.00000 | 0.0733236 | ||||||||
\(745\) | −10.0000 | − | 20.0000i | −0.366372 | − | 0.732743i | ||||
\(746\) | −24.0000 | −0.878702 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | 8.00000i | 0.292509i | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | −11.0000 | − | 2.00000i | −0.401663 | − | 0.0730297i | ||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36.0000 | −1.31104 | ||||||||
\(755\) | −8.00000 | − | 16.0000i | −0.291150 | − | 0.582300i | ||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 32.0000i | 1.16306i | 0.813525 | + | 0.581530i | \(0.197546\pi\) | ||||
−0.813525 | + | 0.581530i | \(0.802454\pi\) | |||||||
\(758\) | 20.0000i | 0.726433i | ||||||||
\(759\) | 16.0000 | 0.580763 | ||||||||
\(760\) | −12.0000 | + | 6.00000i | −0.435286 | + | 0.217643i | ||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | − | 4.00000i | − | 0.144905i | ||||||
\(763\) | 14.0000i | 0.506834i | ||||||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | −8.00000 | + | 4.00000i | −0.289241 | + | 0.144620i | ||||
\(766\) | 20.0000 | 0.722629 | ||||||||
\(767\) | 48.0000i | 1.73318i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 2.00000 | + | 4.00000i | 0.0720750 | + | 0.144150i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.00000i | 0.287926i | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | 6.00000 | − | 8.00000i | 0.215526 | − | 0.287368i | ||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | 4.00000i | 0.143499i | ||||||||
\(778\) | 2.00000i | 0.0717035i | ||||||||
\(779\) | 12.0000 | 0.429945 | ||||||||
\(780\) | 6.00000 | + | 12.0000i | 0.214834 | + | 0.429669i | ||||
\(781\) | −12.0000 | −0.429394 | ||||||||
\(782\) | 32.0000i | 1.14432i | ||||||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | −44.0000 | + | 22.0000i | −1.57043 | + | 0.785214i | ||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | − | 28.0000i | − | 0.998092i | −0.866575 | − | 0.499046i | \(-0.833684\pi\) | ||
0.866575 | − | 0.499046i | \(-0.166316\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | −16.0000 | −0.569615 | ||||||||
\(790\) | 24.0000 | − | 12.0000i | 0.853882 | − | 0.426941i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | − | 60.0000i | − | 2.13066i | ||||||
\(794\) | 2.00000 | 0.0709773 | ||||||||
\(795\) | −6.00000 | − | 12.0000i | −0.212798 | − | 0.425596i | ||||
\(796\) | 6.00000 | 0.212664 | ||||||||
\(797\) | 8.00000i | 0.283375i | 0.989911 | + | 0.141687i | \(0.0452527\pi\) | ||||
−0.989911 | + | 0.141687i | \(0.954747\pi\) | |||||||
\(798\) | 6.00000i | 0.212398i | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 4.00000 | + | 3.00000i | 0.141421 | + | 0.106066i | ||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | 14.0000i | 0.494357i | ||||||||
\(803\) | − | 28.0000i | − | 0.988099i | ||||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 8.00000 | + | 16.0000i | 0.281963 | + | 0.563926i | ||||
\(806\) | −12.0000 | −0.422682 | ||||||||
\(807\) | − | 18.0000i | − | 0.633630i | ||||||
\(808\) | 10.0000i | 0.351799i | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 2.00000 | − | 1.00000i | 0.0702728 | − | 0.0351364i | ||||
\(811\) | −14.0000 | −0.491606 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(812\) | 6.00000i | 0.210559i | ||||||||
\(813\) | 10.0000i | 0.350715i | ||||||||
\(814\) | −8.00000 | −0.280400 | ||||||||
\(815\) | 8.00000 | − | 4.00000i | 0.280228 | − | 0.140114i | ||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | 24.0000i | 0.839654i | ||||||||
\(818\) | 26.0000i | 0.909069i | ||||||||
\(819\) | 6.00000 | 0.209657 | ||||||||
\(820\) | −2.00000 | − | 4.00000i | −0.0698430 | − | 0.139686i | ||||
\(821\) | 22.0000 | 0.767805 | 0.383903 | − | 0.923374i | \(-0.374580\pi\) | ||||
0.383903 | + | 0.923374i | \(0.374580\pi\) | |||||||
\(822\) | 6.00000i | 0.209274i | ||||||||
\(823\) | 12.0000i | 0.418294i | 0.977884 | + | 0.209147i | \(0.0670687\pi\) | ||||
−0.977884 | + | 0.209147i | \(0.932931\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | −8.00000 | − | 6.00000i | −0.278524 | − | 0.208893i | ||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | − | 8.00000i | − | 0.278019i | ||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | −8.00000 | − | 16.0000i | −0.277684 | − | 0.555368i | ||||
\(831\) | 28.0000 | 0.971309 | ||||||||
\(832\) | − | 6.00000i | − | 0.208013i | ||||||
\(833\) | 4.00000i | 0.138592i | ||||||||
\(834\) | 14.0000 | 0.484780 | ||||||||
\(835\) | −24.0000 | + | 12.0000i | −0.830554 | + | 0.415277i | ||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | 2.00000i | 0.0691301i | ||||||||
\(838\) | 20.0000i | 0.690889i | ||||||||
\(839\) | 20.0000 | 0.690477 | 0.345238 | − | 0.938515i | \(-0.387798\pi\) | ||||
0.345238 | + | 0.938515i | \(0.387798\pi\) | |||||||
\(840\) | 2.00000 | − | 1.00000i | 0.0690066 | − | 0.0345033i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | − | 34.0000i | − | 1.17172i | ||||||
\(843\) | 30.0000i | 1.03325i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.0000 | − | 46.0000i | −0.791224 | − | 1.58245i | ||||
\(846\) | 8.00000 | 0.275046 | ||||||||
\(847\) | − | 7.00000i | − | 0.240523i | ||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | −20.0000 | −0.686398 | ||||||||
\(850\) | 12.0000 | − | 16.0000i | 0.411597 | − | 0.548795i | ||||
\(851\) | −32.0000 | −1.09695 | ||||||||
\(852\) | 6.00000i | 0.205557i | ||||||||
\(853\) | 38.0000i | 1.30110i | 0.759465 | + | 0.650548i | \(0.225461\pi\) | ||||
−0.759465 | + | 0.650548i | \(0.774539\pi\) | |||||||
\(854\) | −10.0000 | −0.342193 | ||||||||
\(855\) | −6.00000 | − | 12.0000i | −0.205196 | − | 0.410391i | ||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | − | 24.0000i | − | 0.819824i | −0.912125 | − | 0.409912i | \(-0.865559\pi\) | ||
0.912125 | − | 0.409912i | \(-0.134441\pi\) | |||||||
\(858\) | 12.0000i | 0.409673i | ||||||||
\(859\) | 10.0000 | 0.341196 | 0.170598 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170598 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(860\) | 8.00000 | − | 4.00000i | 0.272798 | − | 0.136399i | ||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | − | 2.00000i | − | 0.0681203i | ||||||
\(863\) | − | 48.0000i | − | 1.63394i | −0.576681 | − | 0.816970i | \(-0.695652\pi\) | ||
0.576681 | − | 0.816970i | \(-0.304348\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −16.0000 | + | 8.00000i | −0.544016 | + | 0.272008i | ||||
\(866\) | −26.0000 | −0.883516 | ||||||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 2.00000i | 0.0678844i | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | −6.00000 | − | 12.0000i | −0.203419 | − | 0.406838i | ||||
\(871\) | 48.0000 | 1.62642 | ||||||||
\(872\) | 14.0000i | 0.474100i | ||||||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | −48.0000 | −1.62362 | ||||||||
\(875\) | 2.00000 | − | 11.0000i | 0.0676123 | − | 0.371868i | ||||
\(876\) | −14.0000 | −0.473016 | ||||||||
\(877\) | 28.0000i | 0.945493i | 0.881199 | + | 0.472746i | \(0.156737\pi\) | ||||
−0.881199 | + | 0.472746i | \(0.843263\pi\) | |||||||
\(878\) | − | 18.0000i | − | 0.607471i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00000 | + | 4.00000i | 0.0674200 | + | 0.134840i | ||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | − | 1.00000i | − | 0.0336718i | ||||||
\(883\) | 24.0000i | 0.807664i | 0.914833 | + | 0.403832i | \(0.132322\pi\) | ||||
−0.914833 | + | 0.403832i | \(0.867678\pi\) | |||||||
\(884\) | −24.0000 | −0.807207 | ||||||||
\(885\) | −16.0000 | + | 8.00000i | −0.537834 | + | 0.268917i | ||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 4.00000i | 0.134231i | ||||||||
\(889\) | 4.00000 | 0.134156 | ||||||||
\(890\) | 20.0000 | − | 10.0000i | 0.670402 | − | 0.335201i | ||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 8.00000i | 0.267860i | ||||||||
\(893\) | − | 48.0000i | − | 1.60626i | ||||||
\(894\) | −10.0000 | −0.334450 | ||||||||
\(895\) | −10.0000 | − | 20.0000i | −0.334263 | − | 0.668526i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 48.0000i | 1.60267i | ||||||||
\(898\) | − | 6.00000i | − | 0.200223i | ||||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | −3.00000 | + | 4.00000i | −0.100000 | + | 0.133333i | ||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | − | 4.00000i | − | 0.133185i | ||||||
\(903\) | − | 4.00000i | − | 0.133112i | ||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 2.00000 | + | 4.00000i | 0.0664822 | + | 0.132964i | ||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | − | 24.0000i | − | 0.796907i | −0.917189 | − | 0.398453i | \(-0.869547\pi\) | ||
0.917189 | − | 0.398453i | \(-0.130453\pi\) | |||||||
\(908\) | − | 8.00000i | − | 0.265489i | ||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | −12.0000 | + | 6.00000i | −0.397796 | + | 0.198898i | ||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 6.00000i | 0.198680i | ||||||||
\(913\) | − | 16.0000i | − | 0.529523i | ||||||
\(914\) | −28.0000 | −0.926158 | ||||||||
\(915\) | 20.0000 | − | 10.0000i | 0.661180 | − | 0.330590i | ||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | − | 12.0000i | − | 0.396275i | ||||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | −60.0000 | −1.97922 | −0.989609 | − | 0.143787i | \(-0.954072\pi\) | ||||
−0.989609 | + | 0.143787i | \(0.954072\pi\) | |||||||
\(920\) | 8.00000 | + | 16.0000i | 0.263752 | + | 0.527504i | ||||
\(921\) | −12.0000 | −0.395413 | ||||||||
\(922\) | 18.0000i | 0.592798i | ||||||||
\(923\) | − | 36.0000i | − | 1.18495i | ||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 16.0000 | + | 12.0000i | 0.526077 | + | 0.394558i | ||||
\(926\) | 36.0000 | 1.18303 | ||||||||
\(927\) | − | 8.00000i | − | 0.262754i | ||||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | −2.00000 | − | 4.00000i | −0.0655826 | − | 0.131165i | ||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | 10.0000i | 0.327561i | ||||||||
\(933\) | 24.0000i | 0.785725i | ||||||||
\(934\) | 24.0000 | 0.785304 | ||||||||
\(935\) | 16.0000 | − | 8.00000i | 0.523256 | − | 0.261628i | ||||
\(936\) | 6.00000 | 0.196116 | ||||||||
\(937\) | − | 26.0000i | − | 0.849383i | −0.905338 | − | 0.424691i | \(-0.860383\pi\) | ||
0.905338 | − | 0.424691i | \(-0.139617\pi\) | |||||||
\(938\) | − | 8.00000i | − | 0.261209i | ||||||
\(939\) | 2.00000 | 0.0652675 | ||||||||
\(940\) | −16.0000 | + | 8.00000i | −0.521862 | + | 0.260931i | ||||
\(941\) | −10.0000 | −0.325991 | −0.162995 | − | 0.986627i | \(-0.552116\pi\) | ||||
−0.162995 | + | 0.986627i | \(0.552116\pi\) | |||||||
\(942\) | 22.0000i | 0.716799i | ||||||||
\(943\) | − | 16.0000i | − | 0.521032i | ||||||
\(944\) | 8.00000 | 0.260378 | ||||||||
\(945\) | 1.00000 | + | 2.00000i | 0.0325300 | + | 0.0650600i | ||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | − | 12.0000i | − | 0.389742i | ||||||
\(949\) | 84.0000 | 2.72676 | ||||||||
\(950\) | 24.0000 | + | 18.0000i | 0.778663 | + | 0.583997i | ||||
\(951\) | −2.00000 | −0.0648544 | ||||||||
\(952\) | 4.00000i | 0.129641i | ||||||||
\(953\) | − | 10.0000i | − | 0.323932i | −0.986796 | − | 0.161966i | \(-0.948217\pi\) | ||
0.986796 | − | 0.161966i | \(-0.0517835\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | −18.0000 | − | 36.0000i | −0.582466 | − | 1.16493i | ||||
\(956\) | 26.0000 | 0.840900 | ||||||||
\(957\) | − | 12.0000i | − | 0.387905i | ||||||
\(958\) | 8.00000i | 0.258468i | ||||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | 2.00000 | − | 1.00000i | 0.0645497 | − | 0.0322749i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | − | 24.0000i | − | 0.773791i | ||||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | 26.0000 | 0.837404 | ||||||||
\(965\) | 16.0000 | − | 8.00000i | 0.515058 | − | 0.257529i | ||||
\(966\) | 8.00000 | 0.257396 | ||||||||
\(967\) | − | 56.0000i | − | 1.80084i | −0.435023 | − | 0.900419i | \(-0.643260\pi\) | ||
0.435023 | − | 0.900419i | \(-0.356740\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | 10.0000 | + | 20.0000i | 0.321081 | + | 0.642161i | ||||
\(971\) | −24.0000 | −0.770197 | −0.385098 | − | 0.922876i | \(-0.625832\pi\) | ||||
−0.385098 | + | 0.922876i | \(0.625832\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 14.0000i | 0.448819i | ||||||||
\(974\) | −12.0000 | −0.384505 | ||||||||
\(975\) | 18.0000 | − | 24.0000i | 0.576461 | − | 0.768615i | ||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | 18.0000i | 0.575871i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) | ||||
−0.957650 | + | 0.287936i | \(0.907031\pi\) | |||||||
\(978\) | − | 4.00000i | − | 0.127906i | ||||||
\(979\) | 20.0000 | 0.639203 | ||||||||
\(980\) | 1.00000 | + | 2.00000i | 0.0319438 | + | 0.0638877i | ||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 30.0000i | 0.957338i | ||||||||
\(983\) | − | 16.0000i | − | 0.510321i | −0.966899 | − | 0.255160i | \(-0.917872\pi\) | ||
0.966899 | − | 0.255160i | \(-0.0821283\pi\) | |||||||
\(984\) | −2.00000 | −0.0637577 | ||||||||
\(985\) | 4.00000 | − | 2.00000i | 0.127451 | − | 0.0637253i | ||||
\(986\) | 24.0000 | 0.764316 | ||||||||
\(987\) | 8.00000i | 0.254643i | ||||||||
\(988\) | − | 36.0000i | − | 1.14531i | ||||||
\(989\) | 32.0000 | 1.01754 | ||||||||
\(990\) | −4.00000 | + | 2.00000i | −0.127128 | + | 0.0635642i | ||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 2.00000i | 0.0635001i | ||||||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | −6.00000 | −0.190308 | ||||||||
\(995\) | −6.00000 | − | 12.0000i | −0.190213 | − | 0.380426i | ||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | 42.0000i | 1.33015i | 0.746775 | + | 0.665077i | \(0.231601\pi\) | ||||
−0.746775 | + | 0.665077i | \(0.768399\pi\) | |||||||
\(998\) | − | 12.0000i | − | 0.379853i | ||||||
\(999\) | −4.00000 | −0.126554 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 210.2.g.b.169.1 | ✓ | 2 | |
3.2 | odd | 2 | 630.2.g.c.379.2 | 2 | |||
4.3 | odd | 2 | 1680.2.t.e.1009.1 | 2 | |||
5.2 | odd | 4 | 1050.2.a.p.1.1 | 1 | |||
5.3 | odd | 4 | 1050.2.a.d.1.1 | 1 | |||
5.4 | even | 2 | inner | 210.2.g.b.169.2 | yes | 2 | |
7.2 | even | 3 | 1470.2.n.b.949.1 | 4 | |||
7.3 | odd | 6 | 1470.2.n.f.79.2 | 4 | |||
7.4 | even | 3 | 1470.2.n.b.79.2 | 4 | |||
7.5 | odd | 6 | 1470.2.n.f.949.1 | 4 | |||
7.6 | odd | 2 | 1470.2.g.b.589.1 | 2 | |||
12.11 | even | 2 | 5040.2.t.h.1009.1 | 2 | |||
15.2 | even | 4 | 3150.2.a.d.1.1 | 1 | |||
15.8 | even | 4 | 3150.2.a.bk.1.1 | 1 | |||
15.14 | odd | 2 | 630.2.g.c.379.1 | 2 | |||
20.3 | even | 4 | 8400.2.a.bp.1.1 | 1 | |||
20.7 | even | 4 | 8400.2.a.w.1.1 | 1 | |||
20.19 | odd | 2 | 1680.2.t.e.1009.2 | 2 | |||
35.4 | even | 6 | 1470.2.n.b.79.1 | 4 | |||
35.9 | even | 6 | 1470.2.n.b.949.2 | 4 | |||
35.13 | even | 4 | 7350.2.a.bk.1.1 | 1 | |||
35.19 | odd | 6 | 1470.2.n.f.949.2 | 4 | |||
35.24 | odd | 6 | 1470.2.n.f.79.1 | 4 | |||
35.27 | even | 4 | 7350.2.a.bz.1.1 | 1 | |||
35.34 | odd | 2 | 1470.2.g.b.589.2 | 2 | |||
60.59 | even | 2 | 5040.2.t.h.1009.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.g.b.169.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
210.2.g.b.169.2 | yes | 2 | 5.4 | even | 2 | inner | |
630.2.g.c.379.1 | 2 | 15.14 | odd | 2 | |||
630.2.g.c.379.2 | 2 | 3.2 | odd | 2 | |||
1050.2.a.d.1.1 | 1 | 5.3 | odd | 4 | |||
1050.2.a.p.1.1 | 1 | 5.2 | odd | 4 | |||
1470.2.g.b.589.1 | 2 | 7.6 | odd | 2 | |||
1470.2.g.b.589.2 | 2 | 35.34 | odd | 2 | |||
1470.2.n.b.79.1 | 4 | 35.4 | even | 6 | |||
1470.2.n.b.79.2 | 4 | 7.4 | even | 3 | |||
1470.2.n.b.949.1 | 4 | 7.2 | even | 3 | |||
1470.2.n.b.949.2 | 4 | 35.9 | even | 6 | |||
1470.2.n.f.79.1 | 4 | 35.24 | odd | 6 | |||
1470.2.n.f.79.2 | 4 | 7.3 | odd | 6 | |||
1470.2.n.f.949.1 | 4 | 7.5 | odd | 6 | |||
1470.2.n.f.949.2 | 4 | 35.19 | odd | 6 | |||
1680.2.t.e.1009.1 | 2 | 4.3 | odd | 2 | |||
1680.2.t.e.1009.2 | 2 | 20.19 | odd | 2 | |||
3150.2.a.d.1.1 | 1 | 15.2 | even | 4 | |||
3150.2.a.bk.1.1 | 1 | 15.8 | even | 4 | |||
5040.2.t.h.1009.1 | 2 | 12.11 | even | 2 | |||
5040.2.t.h.1009.2 | 2 | 60.59 | even | 2 | |||
7350.2.a.bk.1.1 | 1 | 35.13 | even | 4 | |||
7350.2.a.bz.1.1 | 1 | 35.27 | even | 4 | |||
8400.2.a.w.1.1 | 1 | 20.7 | even | 4 | |||
8400.2.a.bp.1.1 | 1 | 20.3 | even | 4 |